I discovered that under three layers of old vinyl tile in a 1954 kitchen, I have hardwood floors. Unfortunately, the first layer of tile was glued with what is now black, very sticky adhesive. Is this a death sentence to refinishing the wooden floors? Any suggestions on removal of the black goo? Thanks in advance.

Your floor will need to be sanded so don't woory too much about damaging from scraping and the use of an adhesive remover. This is your only route that I can see. HOMAX 0221 "JASCO" SEMI-PASTE ADHESIVE REMOVER 1 QT (http://www.acehardwareoutlet.com/(wev0sk551hedpa45do0hb445)/productDetails.aspx?SKU=13740)

I discovered that under three layers of old vinyl tile in a 1954 kitchen, I have hardwood floors. Unfortunately, the first layer of tile was glued with what is now black, very sticky adhesive. Is this a death sentence to refinishing the wooden floors? Any suggestions on removal of the black goo? Thanks in advance.
I found the same stuff on my hardwood floors. After some scraping to get the heavy stuff off I was able to sand and refinish the floors no problem. My wife used an adhesive remover when she scraped the floors. Sorry I don't know what she used, but I'd trust what ballenger suggests.